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arXiv · 0801.3222

Dispersion Relation Bounds for pi pi Scattering

A. V. Manohar·V. Mateu
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Abstract

Axiomatic principles such as analyticity, unitarity and crossing symmetry constrain the second derivative of the pi pi scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations of \bar{l}_1 and \bar{l}_2. We compare our predictions with those derived previously in the literature using similar methods. We compute the one-loop pi pi scattering amplitude in the linear sigma model (LSM) using the MS-bar scheme, a result hitherto absent in the literature. The LSM values for \bar{l}_1 and \bar{l}_2 violate the bounds for small values of m_sigma/m_pi. We show how this can occur, while still being consistent with the axiomatic principles.

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A. V. Manohar, V. Mateu. 2008-05-26. Dispersion Relation Bounds for pi pi Scattering. https://doi.org/10.1103/physrevd.77.094019

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